A174335 - OEIS

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A174335

Upper bound in enumerating what majority decisions are possible with possible abstaining.

0, 16, 256, 2592, 24576, 240000, 2488320, 27659520, 330301440, 4232632320, 58060800000, 850068172800, 13243436236800, 218892235161600, 3827475696844800, 70614415872000000, 1371195958099968000

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OFFSET

0,2

COMMENTS

a(n) from last equations, Larson, p.22.

REFERENCES

J. A. N. d. Condorcet. Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix. L'imprimerie royale, Paris, 1785.

LINKS

Table of n, a(n) for n=0..16.

P. Erdos and L. Moser, On the representation of directed graphs as unions of orderings, Magyar Tud. Akad. Mat. Kutats Int. Kvzl., 9:125-132, 1964.

Paul Larson, Nick Matteo, Saharon Shelah, What majority decisions are possible with possible abstaining, arXiv:1003.2756 [math.CO], 2010.

S. Shelah, What majority decisions are possible, Discrete Mathematics, 309(8): 2349-2364, 2009.

FORMULA

a(n) = 16*(n^3)*(n!) = 16*A000578(n)*A000142(n).

a(n) = 16*A091363(n). - Michel Marcus, Jun 25 2015

EXAMPLE

a(4) = 16*(4^3)*(4!) = 24576.

MATHEMATICA

Table[16n^3 n!, {n, 0, 20}] (* Harvey P. Dale, Feb 25 2016 *)